If a-b=12 and `b/2=10`, what is the value of a+b ?

Options

A. 2
B. 12
C. 32
D. 52

Explanation

To solve the problem step by step, we start with the given equations:

1. **Given equations**:
- \( a - b = 12 \) (Equation 1)
- \( \frac{b}{2} = 10 \) (Equation 2)

2. **Solve for \( b \)**:
From Equation 2, we can find the value of \( b \):
\[ \frac{b}{2} = 10 \]
Multiply both sides by 2:
\[ b = 10 \times 2 = 20 \]

3. **Substitute \( b \) into Equation 1**:
Now that we have \( b = 20 \), we substitute this value into Equation 1:
\[ a - b = 12 \]
Substitute \( b \):
\[ a - 20 = 12 \]

4. **Solve for \( a \)**:
To find \( a \), add 20 to both sides:
\[ a = 12 + 20 = 32 \]

5. **Find \( a + b \)**:
Now we can find \( a + b \):
\[ a + b = 32 + 20 = 52 \]

Thus, the value of \( a + b \) is \( 52 \).